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All the tests, including keys and certificates, are available on Github.
https://github.com/edvinanet/tls-o-matic
That's also where you will find all the current tests while waiting for us to write documentation here.

What is TLS?

"The TLS protocol provides communications security
over the Internet. The protocol allows client/server applications to communicate in a way that is designed to prevent eavesdropping, tampering, or message forgery."
From RFC 5446 that defines the current TLS - version 1.2. Wikipedia is also a good help in explaining TLS.